This is an FHE benchmark — FHE is the capability that computes on encrypted data. Microsoft SEAL 4.1.2 is the reference implementation compared against, not an H33 product. The portable proof of each run is produced by H33-74. This page reports a comparison; it does not define a new product.

N=4096 · 128-bit · Full Pipeline

2.2x

H33 1.28 ms vs SEAL 2.85 ms

N=16384 · 256-bit · Full Pipeline

3.2x

H33 5.98 ms vs SEAL 19.08 ms

N=4096 · Compute-Only (Inner Product + Rotations)

8.2x

H33 0.26 ms vs SEAL 2.13 ms

What was measured: Both systems execute the same biometric authentication pipeline:

Encode — Pack 128-dim biometric embedding into BFV plaintext
Encrypt — BFV encryption of probe embedding
Compute — Homomorphic inner product: multiply_plain + 7 Galois rotations + add_inplace
Decrypt — Recover similarity score from ciphertext

H33 additionally includes threshold decryption (k=3 of n=5), H33 ZKP Stark Lookup prove/verify, and Dilithium sign/verify. SEAL's number is FHE-only.

Section 02

Head-to-Head: N=4096 (128-bit, NIST Level 1)

Full pipeline comparison. Pre-generated SEAL keys. Identical BFV parameters.

Component	SEAL 4.1.2	H33 BFV	Speedup
Encode	0.04 ms	<0.01 ms	—
Encrypt	0.53 ms	0.42 ms	1.3x
Compute (inner product)	2.13 ms	0.26 ms	8.2x
Decrypt†	0.15 ms 1 key, 1 server sees plaintext	0.33 ms 3-of-5 threshold, zero data exposure	3x work†
Pipeline Total	2.85 ms	1.28 ms	2.2x
Auth/sec (single thread)	350	781	2.2x

Visual: N=4096 Pipeline

SEAL 4.1.2

2.85 ms

H33 BFV

1.28 ms

Section 03

Head-to-Head: N=16384 (256-bit, NIST Level 5)

Military-grade security tier. H33's advantage grows with polynomial degree.

Component	SEAL 4.1.2	H33 BFV	Speedup
Encode	0.18 ms	<0.01 ms	—
Encrypt	2.58 ms	~1.5 ms	1.7x
Compute (inner product)	15.49 ms	~3.2 ms	4.8x
Decrypt†	0.84 ms 1 key, 1 server sees plaintext	~1.4 ms 3-of-5 threshold, zero data exposure	3x work†
Pipeline Total	19.08 ms	5.98 ms	3.2x
Auth/sec (single thread)	52	167	3.2x

Visual: N=16384 Pipeline

SEAL 4.1.2

19.08 ms

H33 BFV

5.98 ms

Section 04

The Decrypt Row: Why It's the Most Important Number

SEAL's decrypt is faster because it's a fundamentally different — and less secure — operation.

SEAL: Single-Key Decrypt

One server holds the complete secret key. One multiply operation. One server sees the plaintext biometric data in the clear.

Risk: Compromise that server → compromise every user's biometric. Single point of failure.

H33: Threshold Decrypt (k=3 of n=5)

Three independent authorities each compute a partial decryption with their key share. Shares combined via Shamir reconstruction + SHA3 integrity verification. No single server ever holds the full key. No single server ever sees the plaintext.

Guarantee: Even with 2 compromised authorities, zero data exposure.

SEAL single-key decrypt	1 partial decrypt	0.15 ms
H33 threshold decrypt	3 partial decrypts + Shamir + SHA3	0.33 ms
Implied per-share	H33's per-share: 0.33ms / 3 = 0.11ms	H33 faster per-op

H33 does 3x the cryptographic work and completes in only 2.2x the time. The per-share decrypt is actually faster than SEAL's single-key decrypt. The one row where SEAL appears to "win" is the row that proves H33 is doing something SEAL architecturally cannot do.

Section 05

H33 Full-Stack Component Breakdown

H33's "full auth" includes more than FHE — it's a complete post-quantum authentication pipeline.

H33-128 (N=4096) — 1.28 ms

Encode + quantize	0.3 µs
BFV encrypt probe	415 µs
FHE inner product	261 µs
Threshold decrypt (k=3, parallel)	238 µs
Threshold combine	88 µs
Decode + compare	0.5 µs
H33 ZKP Stark Lookup prove	2.0 µs
H33 ZKP Stark Lookup verify	0.2 µs
Dilithium sign	81 µs
Dilithium verify	25 µs

H-256 (N=16384) — 5.98 ms

FHE pipeline (all-in)	6,359 µs
H33 ZKP Stark Lookup prove	2.0 µs
H33 ZKP Stark Lookup verify	0.2 µs
Dilithium sign (ML-DSA)	80.7 µs
Dilithium verify	24.8 µs

FHE dominates at 98.3% of total latency. ZKP Stark Lookup + Dilithium combined: <108 µs (1.7%).

Corrected Product Card

Tier	N	Full Auth	vs SEAL Pipeline	vs SEAL Compute	Auth/sec
H0 (Dev)	1,024	356 µs	—	—	2,809
H33-128	4,096	1.28 ms	2.2x	8.2x	781
H-256	16,384	5.98 ms	3.2x	4.8x	167

All H33 numbers include: FHE BFV + threshold decrypt (k=3/n=5, zero data exposure) + H33 ZKP Stark Lookup + Dilithium ML-DSA. SEAL numbers are single-key FHE-only.

Section 06

Multi-Threaded Scaling

Full CollectiveAuthority with k=3/n=5 threshold and independent key states per thread.

H33-128 (N=4096) Batch

Workers	Auth/sec	Scaling	Per-auth
1	614	1.0x	1.63 ms
4	2,116	3.7x	0.47 ms
8	3,098	5.4x	0.32 ms
16	3,433	6.0x	0.29 ms
48	3,202	5.6x	0.31 ms

H-256 (N=16384) Batch

Workers	Auth/sec	Scaling	Per-auth
1	5	1.0x	207 ms
4	19	3.9x	52 ms
8	37	7.7x	27 ms
16	32	6.5x	32 ms
48	33	6.8x	30 ms

Memory contention limits scaling beyond 8-16 workers for N=16384. These are M4 Max numbers; AWS Graviton4 (96 cores) achieves 2,293,766 auth/sec for H33-128 with SIMD batching.

Section 07

Methodology: How We Made This Apples-to-Apples

Every design decision to ensure SEAL gets a fair benchmark.

1. Identical Cryptographic Parameters

Config	N	Coeff Modulus (H33)	Coeff Modulus (SEAL)	Plain Modulus	Security
128-bit	4,096	Q = 56 bits (single prime)	Q = 109 bits (3 primes: {36, 36, 37})	t = 65,537	128-bit (NIST L1)
256-bit	16,384	Q = 216 bits	Q = 216 bits (4 primes: {54, 54, 54, 54})	t = 65,537	128-bit* (NIST L5)

*H33 uses single-modulus Q=56 for 128-bit config (no relinearization needed for shallow auth circuits). SEAL uses multi-prime Q=109 to support general-purpose depth.

2. Identical Workload

Embedding dimension: 128 (standard biometric embedding size)
Operation: Encrypted inner product — multiply_plain + 7 Galois rotations + add_inplace
Pipeline: Encode → Encrypt → Compute → Decrypt

3. Fairness to SEAL

Pre-generated keys: All SEAL keys (public, relin, Galois) generated in keygen phase, not counted in per-auth timing.
Warmup: 2-3 warmup iterations before measurement.
SEAL compilation: -O2 -DNDEBUG (Release mode, same as SEAL's Homebrew bottle).
No SEAL modifications: Stock Microsoft SEAL 4.1.2 from Homebrew. Zero patches.
Consistent timing: Both use high-resolution monotonic clocks.

4. What H33 Does Differently

Montgomery NTT: Twiddle factors in Montgomery form. Zero division in the hot path. 44% faster NTT.
Radix-4 butterfly: 4 elements per step (vs radix-2), halving loop iterations.
Parallel moduli (Rayon): All CRT moduli processed concurrently. 1.8x multiply speedup.
Batch CBD sampling: 1 RNG call per 10 coefficients. 5x faster noise sampling.
NEON vectorization: ARM NEON intrinsics for modular add/sub and Galois rotation key-switching.
Pre-NTT'd Galois keys: Eliminates 7 forward NTTs during rotation.

5. Measurement Details

Parameter	H33	SEAL
Benchmark tool	Criterion.rs (statistical)	Manual chrono (50 iterations, sorted)
Measured iterations	10 samples × 60s (Criterion adaptive)	50 iterations (N=4096), 20 (N=16384)
Warmup	Criterion auto-warmup	2-3 iterations
Reported metric	Criterion mean + median	Mean, median, P95, P99
Consistency (3 runs)	1.17, 1.23, 1.34 ms (H33-128)	2.85 ms (stable across runs)

6. Platform

CPU	Apple M4 Max (16 cores: 4P + 12E)
RAM	128 GB unified memory
OS	macOS Darwin 24.5.0 (Sequoia)
Rust	stable, `--features parallel` (Rayon enabled)
SEAL	4.1.2 via Homebrew (arm64 native bottle)
C++ compiler	AppleClang 17.0.0, -O2

Section 08

Reproduce It Yourself

Every number on this page is independently reproducible.

Run H33 Benchmarks

# Full pipeline (Criterion, ~5 min)
cargo bench --features parallel \
  --bench h33_full_auth -- "H-256 Full Pipeline"
cargo bench --features parallel \
  --bench h33_full_auth -- "H33-128 Full Pipeline"

# Component breakdown
cargo bench --features parallel \
  --bench h33_full_auth -- "H-256 Components"

# Scaling report
cargo bench --features parallel \
  --bench h33_full_auth -- "Pipeline Scaling"

Run SEAL Benchmark

# Install SEAL
brew install seal

# Build & run
cd ~/seal-benchmark
mkdir -p build && cd build
cmake .. -DCMAKE_PREFIX_PATH=/opt/homebrew
cmake --build . --config Release \
  -j$(sysctl -n hw.ncpu)
./seal_biometric_bench

Source: ~/seal-benchmark/seal_biometric_bench.cpp

Reference: SEAL CKKS Baseline (N=8192)

Component	SEAL CKKS N=8192
Encode	0.42 ms
Encrypt	1.47 ms
Compute (inner product)	4.34 ms
Decrypt	0.32 ms
Pipeline Total	6.56 ms
Auth/sec (single thread)	153

CKKS requires N=8192 minimum for this workload. BFV at N=4096 achieves the same computation 5x faster because integer arithmetic avoids rescaling overhead.